Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model

The paper uses a series of monthly IBM product revenues to illustrate the usefulness of seasonal fractionally differenced ARMA models for business forecasting. By allowing two seasonal fractional differencing parameters in the model, one at lag three and the other at lag twelve, it obtains a stationary series without losing information about the process behavior through over-differencing. The paper applies modified identification and estimation techniques to the IBM revenue data and compares the resulting model with a specific non-fractional seasonal ARIMA model by looking at each model’s forecasts. The fractionally differenced seasonal model gives more accurate next-quarter, next-half-year, next-year, and next-two-years forecasts than the non-fractional seasonal model based on criteria that are specifically constructed to reflect the accuracy of long-range periodic forecasts.